Ross Taylor (62), Matt Machan with 66 in 70 balls and Harry Finch, with a championship-best 57, all made half-centuries in clearing a deficit of 213 and opening up a lead of 198 when the game ended with their total on 411 for nine.
Contrary to a dismal overnight forecast, a 10-minute delay in the morning was the only disruption from the weather as Sussex set about blunting the home team’s seamers on a pitch
Resuming at 137 for three, still 76 behind, they restricted Worcestershire to two wickets in the morning and two in the afternoon.
Taylor (62) put on 52 with nightwatchman Lewis Hatchett (17) and 48 with Machan, who then added 55 with Finch before he was out for a quick-fire 66 from 70 balls.
Machan’s pull for six off Matt Henry before lunch wiped out the arrears and they were approaching a secure position when Finch and Ben Brown (29) added 60 in 15 overs before tea.
The key to the recovery was Hatchett’s confidence in staying with Taylor through the first hour. When the breakthrough came, it was emphatic, Joe Leach knocking out Hatchett’s off stump as the left hand pushed forward.
To establish some momentum, Worcestershire needed to follow that up straightaway but Taylor carried on to a second half-century for the county in 98 balls.
Henry eventually won a battle between two New Zealanders by bowling Taylor after he had hit nine fours, but Machan was then going well with five fours, as well as his six, on his way to 50 from 40 balls.
In all he batted for 23 overs until wicketkeeper Ben Cox held a one-handed catch from a good delivery by Leach.
As the runs continued to pile up, Worcestershire captain Daryl Mitchell came on to bowl for the first time this season and with his fifth delivery he held a return catch from Finch. This was his first championship wicket in three years.
Henry launched one last effort after tea and in quick succession he trapped Brown in front and had Steve Magoffin (16) caught at mid-off for a final return of four for 122 from 31 overs. He probably deserved better.
Ollie Robinson, unbeaten in the match with scores of 51 and 29, saw out time with last man Stuart Whitingham.
Worcestershire’s director of cricket, Steve Rhodes, said: “I think both teams deserve a lot of credit. Worcestershire for bossing the game. We got a score on the board and made them follow on. Also, you have to take your hat off to the opposition. They dug deep and made life very difficult for us.
“We really tried as hard as we could with the ball and I couldn’t fault the efforts of the bowlers. We went through quite a lot of overs and there were a few tired and sore bodies afterwards.”
Sussex’s head coach, Mark Davis, said: “I think after day one it was going to be hard work. We wanted to see character and skill out there. To get five points out of the game was not easy. We had to grind it out. Leaving with a draw is almost like a win. We played with heart, which is what I am after.”
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